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Estimating the Error Term

With all of my attention devoted to the World Cup coverage in June, I passed over an interesting piece from the weekend edition (June 24) of the Wall Street Journal (subscription required), "Baseball Confronts the Luck Factor." A variety of reseachers are looking at the data. Essentially, its an ultra-micro analysis of every at bat. A summary of the approach used by ProTrade says

ProTrade analyzed detailed data from each batted ball in every Major League game, including speed off the bat and where it landed. Based on typical results for batted balls over each of the last four years with similar characteristics ...

Using this procedure, they compute "lucky" and "unlucky" hits or outs and then recalculate batting averages, ERAs, wins, losses, and other outcomes for players and teams. Sports econ fellow traveler, J.C. Bradbury, garners three paragraphs in the article detailing similar work that he has done. In particular, it mentions his application of these methods to Chipper Jones' seemingly low numbers in 2004 and how they reflected little change in Jones' hitting, just a change in luck.

There are several interesting aspects to this line of research. One is that it indicates that sometimes what we treat as part of a random error term, in fact, grows out of lack of fine-tuned measurements. Dig deeper into measuring things more accurately and the error term shrinks. Ronald Coase might like such a result a lot. Second, there are game-theoretic reactions that complicate the results some. MLB teams do a ton of scouting. When I attend a game, I'm always amazed at how many hard hit balls to the outfield go for outs. To a large extent, the positioning effects are likely randomized over the course of a season. However, the article mentions that the adjustments for "luck" may be influenced where positioning responses are extreme, for example, with a Barry Bonds (or a Willie McCovey in my youth). Last, the applications of these methods are interesting. There is a little addendum to the article listing possible applications and making reference to Malkiel's Random Walk. ProTrade itself hosts a site for buying and selling players.

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